@Shoe - built by Polish king Casimir... doesn't sound natural to me, but I may be wrong.
– user342011Mar 29 at 9:02

1

It sounds natural to me. It is also the most succinct, which may be an advantage. Your second option seems to need a comma after king. But I'll await answers from others who have more time to pursue this interesting issue.
– ShoeMar 29 at 9:15

It depends on what you’re trying to say. That it was an historical person is irrelevant. Compare: sandcastle built by a/the/[null] tourist[,] Touristy Tourist.
– LawrenceMar 29 at 9:21

@Lawrence - It should be a one sentence description of a picture, no other context.
– user342011Mar 29 at 9:25

3 Answers
3

They are all grammatically correct but they have slightly different meanings. This is inevitably a bit subjective but I would say the difference is in which bit is the main information and which bit is the additional information:

ruins of a medieval castle built by the Polish king Casimir the Great
ruins of a medieval castle built by Casimir the Great (who was a Polish King)

We see this structure whenever we want to add extra information to a particular person

the famous George Washington
George Washington (who was famous)

This would not make sense if we said

a famous George Washington

as that would make George Washington and Casimir indefinite.

ruins of a medieval castle built by Polish king Casimir the Great

is a slightly clunkier way of saying the same thing.

On the other hand,

ruins of a medieval castle built by a Polish king Casimir the Great
ruins of a medieval castle built by a Polish King (whose name was Casimir the Great)

Here it is clear that the emphasis is on the fact that the builder was a Polish king (hence the indefinite article), to which we have added his name as an afterthought.

Usually, it would be correct to use the definite form. We know that we're talking about a specific Polish King, whose name was 'Casimir the Great'. When you know that you are referring to a specific person or item, or something that is unique (like the Sun) you would use "the". Unless we know that there are a ton of 'Casimir the Great's, we would use "the".

In case we're not talking about a specific item, or we're introducing an object for the first time in a conversation, you would use an indefinite article, like "I want an apple." If you wanted a specific apple and the other person knew which apple you were talking about, you would say "the apple".

Think of it this way. Definite articles are when you are speaking about something definite, or something exact or defined (just my own little tip for remembering). Indefinite articles are for something that is not declared, or unspecified. In certain contexts, you might find people using an indefinite article before a proper noun, and that's when there might be more people or things with the same name or identity. I remember an occasion when my English teacher said that there was a certain graveyard with records of "a William Shakespeare" or something of the sort. But for your given example, I believe it would be most appropriate to use a definite article.

Notwithstanding anything else, it depends solely on and is governed by the rules for articles as applicable anywhere -- the context and the semantics. All three are grammatically correct and make sense, only they mean different things.